Measuring method of critical current density of superconductor wires using measurement of magnetization loss

ABSTRACT

A method for measuring critical current density of superconductor wires according to the present invention is characterized in that it includes: (a) applying an external magnetic field to the superconductor wires, (b) measuring a magnetization loss of the superconductor wires according to the application of the external magnetic field, (c) normalizing the measured magnetization loss, and then calculating a fully-penetration magnetic field of the superconductor wires according to the normalized magnetization loss, (d) calculating a critical current density of the superconductor wires according to the calculated fully-penetration magnetic field. Therefore, the critical current density of parallel superconductor wires such as stacked superconductor wires may be measured without applying current to the superconductor wires directly.

FIELD OF THE INVENTION

The invention relates to a method for measuring critical current density of superconductor wires using measurement of magnetization loss, in particular to a method for measuring critical current density of superconductor wires by the measurement of the magnetization loss, which is capable of estimating critical current of the superconductor wires using the measured value of the magnetization loss of the superconductor wires.

BACKGROUND OF THE INVENTION

The advent of superconductor wires or high temperature superconductor (HTS) wires triggers the research and development of power appliance using the superconductor wires.

Unlike general power appliances using a copper, the power appliance using the superconductors requires a cooling system to maintain the characteristics of the superconductor wires. Therefore, the superconductor wires must be developed that can be used for the power appliance having high capacity and efficiency so as to secure economical efficiency of the superconductor appliance as compared to general power appliances.

Meanwhile, during the research and development of the power appliance using superconductor wires, the development of laminated wires for the large current application and of split-type wires which are formed by separating superconductor layers electrically for the reduction of AC loss is one of the main techniques that must precede other techniques for the development of power appliances requiring low-loss large current density such as superconductor transformer.

In case of the laminated superconductor wires for large current application and for low loss; however, it is difficult to measure critical current, which is necessary for the evaluation of the characteristics of superconductor wires, since the disproportion of current occurs as to the current distribution into each wire during the measurement through the application of electrical current and thus samples can be damaged.

If it is possible to estimate the density of critical current of superconductor wires without applying current physically, the above problems preferably would be prevented.

DETAILED DESCRIPTION OF THE INVENTION Purpose to be Solved Technically

The present invention is provided to solve the above problem and the purpose is to provide a method for measuring critical current density of superconductor wires using measurement of magnetization loss, capable of measuring critical current density of parallel-type superconductor wires such as laminated superconductor wires, without applying current to the superconductor wires physically.

SUMMARY OF THE INVENTION

The purpose of the invention can be accomplished by a method for measuring critical current density of superconductor wires, comprising (a) applying an external magnetic field to the superconductor wires; (b) measuring a magnetization loss of the superconductor wires according to the application of the external magnetic field; (c) normalizing the measured magnetization loss, and then calculating a fully-penetration magnetic field of the superconductor wires according to the normalized magnetization loss; (d) calculating a critical current density of the superconductor wires according to the calculated fully-penetration magnetic field.

Here, at the step (b), a Brandt's strip model equation may be applied to the calculation for measuring the magnetization loss of the superconductor wires.

The step (c) may comprise (c1) normalizing the measured magnetization loss; (c2) differentiating the normalized magnetization loss; (c3) calculating a fully-penetration magnetic field by determining the relation of the characteristic magnetic field applied to the Brandt's strip model equation and the fully-penetration magnetic field, according to a differentiated value of the normalized magnetization loss.

Furthermore, at the step (c3), the relation of the characteristic magnetic field and the fully-penetration magnetic field may be expressed as an equation B_(d)=β×B_(p), where B_(d) is a characteristic magnetic field, B_(p) is a fully-penetration magnetic field, and β is a ratio of the external magnetic field to the characteristic magnetic field; the β is determined to be the value when the differentiated value of the magnetization loss becomes zero at the step (c2).

Here, at the step (d), the critical current density may be expressed by an equation

${J_{c} = \frac{\beta \; B_{p}\pi}{\mu_{0}d}},$

where J_(c) is a critical current density and d is a width of the superconductor wires.

THE EFFECTS OF THE INVENTION

According to the present invention, a measuring method of critical current density of superconductor wires using measurement of magnetization loss, capable of measuring critical current density of parallel superconductor wires such as stacked superconductor wires, without applying current to the superconductor wires physically is provided.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 represents an example of a magnetization loss measurement system for measuring magnetization loss of superconductor wires in a method for measuring critical current density of superconductor wires using the magnetization loss measurement in accordance with the present invention.

FIG. 2 represents an example of a superconductor wire sample for applying the method of measuring critical current density of superconductor wires using the measurement of magnetization loss in accordance with the present invention.

FIGS. 3 and 4 are graphs showing the measurement of the magnetization loss for the samples of FIG. 2 measured by the system for measuring magnetization loss of FIG. 1.

FIGS. 5 and 6 are graphs showing the measurement of normalized magnetization loss for the magnetization loss of FIGS. 3 and 4, respectively.

FIG. 7 represents an example for the differentiated value of the normalized magnetization loss.

DESCRIPTION OF THE BEST EMBODIMENT

The method for measuring critical current density of superconductor wires according to the present invention is characterized in that it comprises (a) applying an external magnetic field to the superconductor wires; (b) measuring a magnetization loss of the superconductor wires according to the application of the external magnetic field; (c) normalizing the measured magnetization loss, and then calculating a fully-penetration magnetic field of the superconductor wires according to the normalized magnetization loss; (d) calculating a critical current density of the superconductor wires according to the calculated fully-penetration magnetic field.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Embodiments of the invention will now be described in detail with reference to the accompanying drawings hereinafter.

The method for measuring critical current density of superconductor wires (100) comprises the application of the external magnetic field to the superconductor wires, the measurement of the magnetization loss of the superconductor wires according to the application of the external magnetic field, and the calculation of the critical current density of the superconductor wires (100) by the measured magnetization loss.

More precisely, external magnetic field is applied to the superconductor wires (100) to be measured, and the magnetization loss of the superconductor wires (100) by the application of the external magnetic field is measured. FIG. 1 shows exemplarily a magnetization loss measurement system for measuring magnetization loss of superconductor wires (100) in a method for measuring critical current density of superconductor wires (100) in accordane with the present invention.

As shown in FIG. 1, the magnetization loss measurement system comprises a pair of magnets (10 a, 10 b) for the application of external magnetic field, and a power supply (60) for providing the pair of magnets (10 a, 10 b) with power such that magnetic field is generated between a pair of magnets (10 a, 10 b) and then the external magnetic field is applied to the superconductor wires (100).

Here, the superconductor wires (100) is located in a pick-up coil (20), and when the external magnetic field is applied, the voltage induced to the pick-up coil (20) is generated by the sum of the magnetic field from the superconductor wires (100) and the external magnetic field. Therefore, to obtain only the magnetic field from the superconductor wires (100), the induced electromotive force by the external magnetic field is compensated by the connection of the compensation coils (30) having the same turns as the pick-up coils (20) to the pick-up coils (20).

The system for measuring the magnetization loss comprises a pair of isolation amplifier (40 a, 40 b) and a digital measuring device such as an oscilloscope (50), as shown in FIG. 1. In accordance with the above constitution, by the application of the external magnetic field to the superconductor wires (100), the magnetization loss of the superconductor wires (100) is determined by the inflow and outflow of generated energy. Here, the magnetization loss per a unit length, per a cycle is expressed as the following [Equation 1].

Q _(m)=

{right arrow over (E)}×{right arrow over (H)}·{right arrow over (ds)}  [Equation 1]

Here, {right arrow over (E)} is an electric field generated along the superconductor wires (100), and {right arrow over (H)} is an intensity of the magnetic field according to the external magnetic field.

Also, the following [Equation 2] can be derived by expressing the [Equation 1] in the form of the magnetization loss of the superconductor wires (100) per a unit volume, per a cycle, using the measured voltage and current.

$\begin{matrix} {Q_{m} = {\frac{C_{pu}k}{V_{s}}{\int_{0}^{T}{{\upsilon (t)}{i(t)}{t}}}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack \end{matrix}$

Here, k is a magnetic constant representing magnetic flux density per unit current of the magnet (10 a, 10 b) used to generate the external magnetic field, and C_(pu) is a correction constant of the pick-up coils (20), and V_(s) is a volume of the superconductor wires (100), and T is a period.

Using the above constitution, an experiment to measure the magnetization loss of the superconductor wires (100) was performed. The detailed specifications of the superconductor wires (100) used for the experiment to measure the magnetization loss is shown in the following [Table 1], and the shape of the superconductor wires (100) is shown in the FIG. 2.

TABLE 1 Sample1 Sample2 Sample3 Sample4 Type SF12050 SCS12050 SCS4050 344C Width 12 12 4 4.3 [mm] Thickness 0.05 0.095 0.095 0.2 [mm] Stabilizer — Cu, 40 μm Cu, 40 μm Cu, 100 μm Substrate Hastelloy Hastelloy Hastelloy Ni5% W Sample5 Sample6 Sample7 Sample8 Type F1_N1_4.5 F1_N1_5.3 F2_N1_5.3 F1_N2_5.3 Width 4.5 5.3 5.3 10.6 [mm] Thickness 0.05 0.05 0.05 0.05 [mm] Stabilizer — — — — Substrate Hastelloy Hastelloy Hastelloy Hastelloy

Here, samples are provided such as superconductor wires (100) comprising a copper stabilizing layer and being 12 mm and 4 mm in width, superconductor wires (100) having no copper stabilizing layer and being 12 mm in width, superconductor wires (100) having a copper stabilizing layer and being 4.3 mm in width, three types of wires for transposition stacked wires and one type of stacked wire that are prepared for low-loss stacked wires for large current. The wires for transposition stacked wires are prepared in such a manner that wires having a copper stabilizing layer and being 12 mm in width are cut into wires having width of 4.5 mm and 5.3 mm.

FIG. 3 is a graph showing measured value of the magnetization loss for the samples 1 to 4 according to the measuring method as explained above, and FIG. 4 is a graph showing the measured value of the magnetization loss for the samples 5 to 8 according to the measuring method as explained above.

Hereinafter, a method for measuring the critical current density of the superconductor wires (100) using magnetization loss of the superconductor wires (100) measured by the above process.

The present invention uses Brandt's strip modeling equation shown in the following [Equation 3], for the calculation of magnetization loss by external magnetic field applied in the vertical direction of the superconductor wires (100).

$\begin{matrix} {Q_{m} = {\frac{2\; B_{m}^{2}}{\mu_{0}}{\frac{\pi\omega}{2\; \beta \; d}\left\lbrack {{\frac{2}{\beta}{\ln \left( {\cosh \; \beta} \right)}} - {\tanh \; \beta}} \right\rbrack}}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack \end{matrix}$

Here, B_(m) is a dimension for the external magnetic field, and d is a width of the superconductor wires (100). β is a ratio of the external field to the characteristic magnetic field, which can be defined in the following [Equation 4].

$\begin{matrix} {\beta = \frac{B_{m}}{B_{d}}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack \end{matrix}$

Here, B_(d) represents a dimension of the characteristic magnetic field, which can be defined as the following [Equation 5].

$\begin{matrix} {B_{d} = \frac{\mu_{0}J_{c}d}{\pi}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack \end{matrix}$

Here, Jc is a critical current density of the superconductor wires (100).

If the Brandt's strip model equation in the equation 3 is normalized to confirm a fully-penetration magnetic field, it can be expressed as the following equation 6.

$\begin{matrix} \begin{matrix} {{{Normalized}\mspace{14mu} {loss}} = {\frac{2\pi \; w}{d\; \beta}\left\lbrack {{\frac{2}{\beta}{\ln \left( {\cosh \; \beta} \right)}} - {\tanh \; \beta}} \right\rbrack}} \\ {= {K{\frac{1}{\beta}\left\lbrack {{\frac{2}{\beta}{\ln \left( {\cosh \; \beta} \right)}} - {\tanh \; \beta}} \right\rbrack}}} \end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack \end{matrix}$

In the [Equation 6],

$\frac{2\pi \; w}{d}$

can be defined as a constant K. If the normalized equation 6 is differentiated with regard to β, it can be expressed as the following [Equation 7]. Here, FIGS. 5 and 6 are graphs showing the measured value of normalized magnetization loss for the magnetization loss of FIGS. 3 and 4, respectively, and FIG. 7 shows an example for the differentiated value of the normalized magnetization loss.

As exemplarily illustrated in FIG. 7, it can be seen that β is 2.4642 when a differentiated value of the normalized magnetization loss becomes zero. Therefore, in case that critical current density is calculated using the fully-penetration magnetic field from the normalized magnetization loss, if the critical current density is calculated with the value of β being 2.4642, the following [Equation 8] can be obtained.

$\begin{matrix} {{{Differentiated}\mspace{14mu} {value}} = {{{- \frac{4}{\beta^{3}}}{\ln \left( {\cosh (\beta)} \right)}} + {\frac{3}{\beta^{2}}{\tanh (\beta)}} - \frac{1}{{\beta cosh}^{2}(\beta)}}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack \\ {\mspace{79mu} {B_{d} = {2.4642 \times B_{p}}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack \end{matrix}$

As above, if the fully-penetration magnetic field is determined, it is possible to predict the critical current density of the superconductor wire's (100) as in the following [Equation 9].

$\begin{matrix} {J_{c} = \frac{2.4642\; B_{p}\pi}{\mu_{0}d}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack \end{matrix}$

By normalizing and differentiating the Brandt's strip model equation that expresses the magnetization loss so as to obtain a fully-penetration magnetic field required to calculate the critical current density, it is possible to define the relation of the fully-penetration magnetic field and the characteristic magnetic field used for the Brandt's strip model equation and thus to measure the critical current density.

[Table 2] shows the difference of the critical current density for each sample of [Table 1] calculated by the method for measuring critical current density of superconductor wires (100) according to the invention, and the critical current density measured physically.

As shown in the [Table 2], the critical current density for the samples from the method for measuring the critical current density of the superconductor wires (100) is identical to the physically measured critical current density within the error range approximately less than 5%. Meanwhile, it can be seen that the sample 4 causes 45% error, and this is because wires of the sample 4 use Ni5% W substrate as shown in the [Table 1] and therefore, the magnetic body influences the measurement of the magnetization loss.

TABLE 2 Estimated value of Measured value of critical current critical current Error Sample 1 27.7 A/m² 28.6 A/m² 3.2% Sample 2 26.3 A/m² 24.8 A/m² 6% Sample 3 33.8 A/m² 34.0 A/m² 0.6% Sample 4 29.8 A/m² 20.5 A/m² 45% Sample 5 27.3 A/m² 26.8 A/m² 1.9% Sample 6 27.7 A/m² 27.9 A/m² 0.7% Sample 7 27.3 A/m² 25.7 A/m² 5.8% Sample 8 21.5 A/m² 22.0 A/m² 2.3%

The preferred embodiments of the invention are described above, but it should be understood by those skilled in the art that various modifications and alterations may occur depending on the aspects of the present invention defined in the appended claims insofar as they are within the scope of the present invention or the equivalents thereof. 

1. A method for measuring critical current density of superconductor wires, the method comprising: (a) applying an external magnetic field to the superconductor wires; (b) measuring a magnetization loss of the superconductor wires, according to the application of the external magnetic field; (c) normalizing the measured magnetization loss, and then calculating a fully-penetration magnetic field of the superconductor wires according to the normalized magnetization loss; and (d) calculating a critical current density of the superconductor wires according to the calculated full-penetration magnetic field.
 2. The method for measuring critical current density of superconductor wires of claim 1, wherein, at (b), a Brandt's strip model equation is applied to the calculation for measuring the magnetization loss of the superconductor wires.
 3. The method for measuring critical current density of superconductor wires of claim 2, wherein (c) comprises: (c1) normalizing the measured magnetization loss; (c2) differentiating the normalized magnetization loss; and (c3) calculating a full-penetration magnetic field by determining a relation of the characteristic magnetic field applied to the Brandt's strip model equation and the full-penetration magnetic field, according to a differentiated value of the normalized magnetization loss.
 4. The method for measuring critical current density of superconductor wires of claim 3, wherein: at (c3), the relation of the characteristic magnetic field and the full-penetration magnetic field is expressed as an equation B_(d)=β×B_(p), where B_(d) is a characteristic magnetic field, B_(p) is a full-penetration magnetic field, and β is a ratio of the external magnetic field to the characteristic magnetic field; and the β is determined to be the value when the differentiated value of the magnetization loss becomes zero at (c2).
 5. The method for measuring critical current density of superconductor wires of claim 4, wherein, at (d), the critical current density is expressed by an equation ${J_{c} = \frac{\beta \; B_{p}\pi}{\mu_{0}d}},$ where J_(c) is a critical current density, and d is a width of the superconductor wires. 